I'm not aware of any freely available host models. There are host controllers, but they still would require you to implement the whole application logic.
Linux is definitely better for testing. If you are making an HID device, then no drivers necessary, OS will just use native HID drivers. You may actually have better control over the process with a microcontroller with a USB host controller. That way you will be able to see all the steps of the process and compare operation with other off the shelf HID devices.
Hardware USB analyses are pretty expensive. Some sort of way to sniff the bus is definitely necessary. But what specifically depends on what exactly you want to implement. For USB HS you need a real PHY and a real sniffer, for sure. For USB FS or LS, you can get away with reasonable fast logic analyzer with corresponding protocol decoder.
For USB LS FPGA will be able to just bit bang the protocol, just like V-USB does on AVRs. This is very easy to do, and you can use V-USB as a reference.
For USB FS bit banging is still an option, but you would need to be much more careful about your timings.
Note that in both cases you may not meet requirements of the USB specification to the electrical signaling, but in practice it will work. You won't be able to certify your device with USB, but I assume you don't need that anyway.
There is a complete hardware-only implementation of the USB CDC out there. But typically people use some sort of a soft core to implement the actual protocol logic.